Efficient Randomness Extraction in Quantum Random Number Generators

  • Maurício J. Ferreira University of Aveiro
  • Nuno A. Silva University of Aveiro
  • Nelson J. Muga University of Aveiro


Randomness extraction algorithms play an essential role in Quantum Random Number Generators (QRNGs), where they are used to suppress unwanted classical noise and distill true randomness from their biased output. By employing the SHA-512 hash function and Toeplitz matrix multiplication, we analyse two suitable constructions based on different principles and reach postprocessing rates of 8.69 Mbps and 3.68 Mbps, respectively. Finally, we develop a length-compatible Toeplitz-hashing algorithm able to achieve rates of 143.29 Mbps in a parallelized GPU implementation.


Bouda, J., Pivoluska, M., Plesch, M., and Wilmott, C. (2012). Weak randomness seriously limits the security of quantum key distribution. Phys. Rev. A, 86:062308.

Ferreira, M. J., Silva, N. A., Pinto, A. N., and Muga, N. J. (2021a). Characterization of a quantum random number generator based on vacuum fluctuations. Applied Sciences, 11(16).

Ferreira, M. J., Silva, N. A., Pinto, A. N., and Muga, N. J. (2021b). Homodyne noise characterization in quantum random number generators. In 2021 Telecoms Conference (ConfTELE), pages 1-6, Leiria, Portugal.

Guo, Y., Cai, Q., Li, P., Jia, Z., Xu, B., Zhang, Q., Zhang, Y., Zhang, R., Gao, Z., Shore, K. A., and Wang, Y. (2021). 40 gb/s quantum random number generation based on optically sampled amplified spontaneous emission. APL Photonics, 6(6):066105.

Haw, J. Y., Assad, S. M., Lance, A. M., Ng, N. H. Y., Sharma, V., Lam, P. K., and Symul, T. (2015). Maximization of extractable randomness in a quantum random-number generator. Phys. Rev. Applied, 3:054004.

Hayashi, M. and Tsurumaru, T. (2016). More efficient privacy amplification with less random seeds via dual universal hash function. IEEE Transactions on Information Theory, 62(4):2213-2232.

Herrero-Collantes, M. and Garcia-Escartin, J. C. (2017). Quantum random number generators. Rev. Mod. Phys., 89:015004.

Huang, M., Chen, Z., Zhang, Y., and Guo, H. (2020). A phase fluctuation based practical quantum random number generator scheme with delay-free structure. Applied Sciences, 10(7).

Kelsey, J., Schneier, B., Wagner, D., and Hall, C. (1998). Cryptanalytic attacks on pseudorandom number generators. In Vaudenay, S., editor, Fast Software Encryption, pages 168-188, Berlin, Heidelberg. Springer Berlin Heidelberg.

Knuth, D. E. (1998). The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, 3 edition.

Koç, Ç. (2015). Open Problems in Mathematics and Computational Science. Springer International Publishing.

Ma, X., Xu, F., Xu, H., Tan, X., Qi, B., and Lo, H.-K. (2013). Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction. Phys. Rev. A, 87:062327.

National Institute of Standards and Technology (NIST) (2015). Secure Hash Standard (SHS) (FIPS PUB 180-4). Federal Information Processing Standards Publication, 180-4(August):36.

Nie, Y.-Q., Huang, L., Liu, Y., Payne, F., Zhang, J., and Pan, J.-W. (2015). The generation of 68 Gbps quantum random number by measuring laser phase fluctuations. Review of Scientific Instruments, 86(6):063105.

Vadhan, S. P. (2012). Pseudorandomness. Foundations and Trends in Theoretical Computer Science, 7(1-3):1-336.

Wang, X., Zhang, Y., Yu, S., and Guo, H. (2018). High-speed implementation of length-compatible privacy amplification in continuous-variable quantum key distribution. IEEE Photonics Journal, PP:1-1.
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FERREIRA, Maurício J.; SILVA, Nuno A.; MUGA, Nelson J.. Efficient Randomness Extraction in Quantum Random Number Generators. In: WORKSHOP DE COMUNICAÇÃO E COMPUTAÇÃO QUÂNTICA (WQUANTUM), 2. , 2022, Fortaleza. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 31-36. DOI: https://doi.org/10.5753/wquantum.2022.223591.